The Better Half of Mathematics

Article excerpt

Isaac Newton showed no signs of being a brilliant child, only an odd one. Reading books when he should have been tending sheep, fond of small inventions, isolated and tearful; 'In the top of the house - in the bottom of Hell,' he wrote, aged ten, in his Latin exercise book. What employment was he fit for? he wondered. On another page, under the rubric, 'Things Hurtfull for the Eyes', he listed: 'Gooing too suddaine after meals. Hot wines. Cold ayre ... much weeping.' He drew charcoal circles and triangles on the walls of his attic bedroom.

The plague years of 1664-6 uncovered Newton's genius. Then a student at Cambridge, he fled back to his mother's isolated farm in Woolsthorpe for his own safety, opened yet another notepad, this one 1,000 pages long, named it his 'Waste Book' and began a furious piece of work in 16th of an inch-high lettering. On one page he calculated the area under a hyperbola and - as James Gleick puts it in this entertaining, evocative, casual biography - 'stepped past the algebra Descartes knew'. On another page, he conceived of infinite series 'transforming the state of mathematics'. It is rather pleasing to find, on the frontispiece reproduction of a page from his notebooks, that Newton has got a sum wrong.

His great talent was to discover simplicity and generalisations. As for the infinitesimal, the basis of calculus, I remember the teasing smile on my teacher's face when he first put the notion of this tiny monster to our A-level mathematics class: something that was as small as you could ever wish it to be, with no set value, just 'tending' to zero, but not zero. I'm glad to say Newton suffered agonies inventing the idea. When he returned to the university he was 24. His great friend (and, later, rival) Leibnitz said that the history of mathematics could be divided into the centuries leading up to Newton and Newton himself; and Newton represented the better half.

But Newton refused to publish. His work seemed almost to bore him. Why? One of the great pleasures of this short book is that it provokes so many enjoyable questions (although, once or twice, Gleick's lack of opinion about possible answers makes one want to give him a slap). …